Well-known equations for analysis of large displacements of flexible rods were checked for compatibility with the law of energy conservation. The requirement for such verification arose because of appearance in computational practice a number of problems in rod mechanics where axial deformations account is necessary (rods made of elastomers, shape memory materials, etc.). To test the problematic equations, a numerical experiment was conducted in this paper: the boundary value problem of loading a semi-circular arch with a concentrated force was solved using standard procedures of a computer mathematics package. Based on the set of solutions for different force values, mechanical work of force was calculated, and for the final position of the arch, the strain energy was determined. The mechanical work did not match the strain energy, therefore the controlled equations were found erroneous. The error occurred due to an incorrect elasticity ratio for the bending moment. The problematic equations did not take into account the fact that the curvature of the rod changes for two reasons: (1) due to rotations of the axis, (2) due to deformations of the axis. After correcting the error, the adjusted differential equations successfully passed the verification for compliance with the law of energy conservation. Two variants of corrected equations for flat bending problem of rod which axial deformation account are provided and recommended for practical application.

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